A calibration and parameter estimation method, apparatus, and radar system for an FDA-MIMO radar.

Abstract

This invention discloses a calibration and parameter estimation method for FDA-MIMO radar, comprising: acquiring the echo signal received by each receiving array element and performing matched filtering to obtain all received signals; calculating the covariance matrix of the received signals and performing eigenvalue decomposition to obtain the noise subspace of the received signals; estimating the target angle and range based on the noise subspace using a dimensionality reduction peak search method; obtaining the eigenvector corresponding to the minimum eigenvalue of the angle-range joint peak search function; constructing a new matrix from the eigenvectors and performing singular value decomposition on the constructed new matrix, and finding the left and right singular value vectors corresponding to the maximum singular value in the obtained left and right singular matrices, and estimating the amplitude and phase errors of the transmitting and receiving arrays. This method has the ability to estimate targets with high accuracy even in the presence of amplitude and phase errors.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a calibration and parameter estimation method, device, and radar system for FDA-MIMO radar. Background Technology

[0002] With the continuous advancement of electronic devices and the increasing complexity of environments, traditional phased array radars may fail to meet target localization requirements in certain scenarios. FDA (Frequency Diverse Array) radar is a relatively new radar system that has emerged in recent years. Multiple-input multiple-output (MIMO) radar is characterized by multiple antennas simultaneously transmitting orthogonal waveforms and multiple antennas receiving reflected signals. FDA-MIMO radar, which combines FDA and MIMO radars, not only enjoys the spatial diversity advantages of MIMO radar but also possesses controllable range dimensions, enabling target localization in complex environments.

[0003] Currently, radar target parameter estimation is one of the important tasks in radar target detection in radar signal processing. Traditional methods such as Multiple Signal Classification (MUSIC), Estimating Signal Parameters via Rotational Invariance Techniques (ESPRIT), and Real-Valued ESPRIT work effectively under ideal conditions where the array antenna has no amplitude and phase errors.

[0004] However, in practice, each transmit or receive antenna in the array corresponds to a transmit or receive channel, and each channel contains multiple active devices. As these active devices operate over time, they gradually experience wear and aging, causing changes in their amplitude and phase characteristics. Furthermore, environmental factors, such as temperature variations, also affect the amplitude and phase characteristics of the active devices. Therefore, these factors introduce amplitude and phase errors into the radar system, independent of the target angle, thus impacting the radar's positioning performance. Especially for FDA-MIMO radars with random amplitude and phase errors, existing parameter estimation methods have low accuracy and may even fail. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention provides a calibration and parameter estimation method, apparatus, and radar system for FDA-MIMO radar. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] In a first aspect, the present invention provides a calibration and parameter estimation method for FDA-MIMO radar, comprising:

[0007] Step 1: Obtain the echo signal received by each receiving array element and perform matched filtering to obtain all received signals;

[0008] Step 2: Calculate the covariance matrix of the received signal and perform eigenvalue decomposition to obtain the noise subspace of the received signal;

[0009] Step 3: Construct an angle-dimensional spectral peak search function based on the noise subspace, and perform a dimensionality-reduced spectral peak search to obtain the target angle estimate;

[0010] Step 4: Construct an angle-distance joint spectral peak search function based on the angle estimation, and perform spectral peak search to obtain the target distance estimate;

[0011] Step 5: Obtain the eigenvector corresponding to the minimum eigenvalue of the angle-distance joint spectral peak search function;

[0012] Step 6: Construct a new matrix from the eigenvectors, and perform singular value decomposition on the constructed new matrix to obtain left and right singular matrices;

[0013] Step 7: Find the left and right singular value vectors corresponding to the largest singular value in the left and right singular matrices, and estimate the amplitude and phase errors of the transmit and receive arrays.

[0014] Secondly, the present invention provides a calibration and parameter estimation apparatus for FDA-MIMO radar, comprising:

[0015] The matched filtering module is used to acquire the echo signal received by each receiving array element and perform matched filtering to obtain all received signals.

[0016] The first calculation module is used to calculate the covariance matrix of the received signal and perform eigenvalue decomposition to obtain the noise subspace of the received signal.

[0017] An angle estimation module is used to construct a spectral peak search function in the angle dimension based on the noise subspace, and perform a spectral peak search after dimensionality reduction transformation to obtain the angle estimate of the target;

[0018] The distance estimation module is used to construct an angle-distance joint spectral peak search function based on the angle estimation, and to perform spectral peak search to obtain the target distance estimate;

[0019] The second calculation module is used to obtain the feature vector corresponding to the minimum feature value of the angle-distance joint spectral peak search function;

[0020] The singular value decomposition module is used to construct a new matrix from the eigenvectors and perform singular value decomposition on the constructed new matrix to obtain left and right singular matrices.

[0021] The error estimation module is used to find the left and right singular value vectors corresponding to the maximum singular value in the left and right singular matrices, and to perform error estimation of the amplitude and phase of the transmit and receive arrays.

[0022] Thirdly, the present invention provides an FDA-MIMO radar system, comprising M transmitting elements and N receiving elements, wherein the M transmitting elements are used to transmit orthogonal signals toward a target, and the N receiving elements are used to receive echo signals returned from the target.

[0023] The radar system further includes: a processor, a communication interface, a memory, and a communication bus; wherein,

[0024] The processor, communication interface, and memory communicate with each other through a communication bus;

[0025] Memory is used to store computer programs;

[0026] When the processor executes a program stored in memory, it implements the steps of the method described in the above embodiments.

[0027] The beneficial effects of this invention are:

[0028] This invention proposes a calibration and parameter estimation method for FDA-MIMO radar with random amplitude and phase errors. First, by calculating the covariance matrix of the received signal and performing eigenvalue decomposition, the noise subspace of the signal can be obtained. Then, a dimension-reduced peak search method is used to estimate the target angle and range. Finally, by performing singular value decomposition on the sum matrix of the angle-range joint peak search function, the left and right singular vectors corresponding to the maximum singular values ​​are obtained, thus yielding the amplitude and phase error estimates. This method has the ability to estimate targets with high accuracy even in the presence of amplitude and phase errors.

[0029] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0030] Figure 1 A flowchart illustrating a calibration and parameter estimation method for an FDA-MIMO radar provided in an embodiment of the present invention;

[0031] Figure 2 A signal transceiver model diagram of an FDA-MIMO radar system provided in an embodiment of the present invention;

[0032] Figure 3A structural block diagram of a calibration and parameter estimation device for an FDA-MIMO radar provided in an embodiment of the present invention;

[0033] Figure 4 The figure shows the estimation results for a three-target scenario in the far field during the simulation experiment.

[0034] Figure 5 The figure shows the amplitude error estimation results of the transmitting array element in the simulation experiment;

[0035] Figure 6 The figure shows the phase error estimation results of the transmitting array element in the simulation experiment;

[0036] Figure 7 The figure shows the amplitude error estimation results of the receiving array element in the simulation experiment;

[0037] Figure 8 The figure shows the phase error estimation results of the receiving array element in the simulation experiment;

[0038] Figure 9 The root mean square error (RMSE) plot of distance versus signal-to-noise ratio in the simulation experiment;

[0039] Figure 10 The root mean square error (RMSE) plot of angle and signal-to-noise ratio in the simulation experiment is shown.

[0040] Figure 11 This is a graph showing the relationship between the root mean square error of distance and the number of snapshots in the simulation experiment;

[0041] Figure 12 This is a graph showing the relationship between the root mean square error of the angle and the number of snapshots in the simulation experiment. Detailed Implementation

[0042] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0043] Example 1

[0044] Please see Figure 1 , Figure 1 This is a flowchart illustrating a calibration and parameter estimation method for an FDA-MIMO radar provided in an embodiment of the present invention. This method addresses the parameter estimation problem of FDA-MIMO radar with random amplitude and phase errors, and specifically includes the following steps:

[0045] Step 1: Obtain the echo signal received by each receiving array element and perform matched filtering to obtain all received signals.

[0046] In this embodiment, a signal transmission and reception model of an FDA-MIMO radar under random amplitude and phase errors of array elements is established, and the transmitted and received signals under this model are obtained. Figure 2As shown, Figure 2 A signal transmission and reception model diagram of a juxtaposed FDA-MIMO radar system is shown, which includes M transmitting antennas and N receiving antennas. It is assumed that the number of transmitting antennas without amplitude loss is L. T The number of receiving antennas without phase loss is L. R .

[0047] First, M transmitting array elements transmit orthogonal signals.

[0048] Specifically, in this invention, the amplitude and phase errors of the affected antennas are considered unknown and random. All antennas transmit and receive isotropic, uniform, and omnidirectional electromagnetic waves. To avoid aliasing of the sampled signals, the spacing between all adjacent elements needs to be placed to half the maximum wavelength. This invention considers independent far-field targets and selects a first antenna as a reference.

[0049] Furthermore, to ensure effective separation of each transmit channel in the receiver, M transmit array elements are required to transmit orthogonal signals. Also, the FDA-MIMO radar uses a small frequency increment between array elements; the carrier frequency of the m-th element is:

[0050] f m =f1+(m-1)Δf,m=1,2,…,M;

[0051] Where f1 and Δf represent the carrier frequency of the reference antenna and the frequency offset between adjacent antennas, respectively. This means that the frequency variation between adjacent antennas is uniform. Typically, this frequency increment is much smaller than the reference carrier frequency, therefore, it has the following approximate expression:

[0052]

[0053] Where c represents the speed of light, θ represents the angle of the target, r represents the distance to the target, Δf represents the frequency offset between adjacent antennas, and d t This indicates the spacing between the elements of the emission array.

[0054] Then the m-th signal radiated by each transmitting antenna after baseband modulation and carrier loading can be expressed as:

[0055]

[0056] In the formula, E is the radar's transmit power. Let T be the baseband signal of the m-th signal. w This represents the pulse width.

[0057] It should be noted that, in order to avoid echo fluctuations, the transmitted signal satisfies the narrowband assumption, that is, the baseband signals of the M transmitting elements satisfy the following equation:

[0058]

[0059] Where τ and * represent the time delay and conjugate transpose, respectively.

[0060] Then, the N receiving array elements use the mutual orthogonality of orthogonal signals to perform matched filtering on the reflected echo signal of the target to obtain the filtered received signal.

[0061] Specifically, in this embodiment, the first transmitting element and the receiving element are considered as reference elements. In this invention example, the far-field target is assumed to be a point target. The output of each receiving element is the superposition of all transmitted signals at that element. For the orthogonal signals emitted by the m-th transmitting element, the time delay of the n-th receiving element relative to the m-th transmitting element can be expressed as:

[0062]

[0063] To separate the M transmitted signals, each received echo must pass through M matched filters during reception processing. Therefore, the output of the nth noise-free processing channel can be expressed as:

[0064]

[0065] In the formula, m∈[1,M], M represents the number of transmitting array elements, n∈[1,N], N represents the number of receiving array elements, f0 represents the carrier frequency, and d t and d r ξ represents the spacing between the elements of the transmitting and receiving arrays; ξ is the complex coefficient of the target, including electromagnetic wave propagation, target backscattering, pulse compression processing gain, etc.

[0066] The vector form r of the filtered received signal s Represented as:

[0067]

[0068] in,[.] T Let a represent the transpose operator. TR The Kronecker product of the transmit and receive steering vectors with amplitude and phase errors is given, where n represents white noise and C represents the white noise. R and C T The diagonal matrix representing the amplitude and phase errors contained in the receiving and transmitting arrays. Represents the Kronecker product, a R (θ) and a T (θ, r) are the transmit and receive direction vectors, respectively, and are expressed as:

[0069]

[0070]

[0071] As can be seen from the calculation formula of the transmit steering vector, the angle and range parameters are naturally coupled. Therefore, a corresponding decoupling method must be used when estimating the parameters. In this invention, since the angle estimation parameters can be obtained first, decoupling can be achieved by substituting the obtained angle estimate into the corresponding received data.

[0072] Step 2: Calculate the covariance matrix of the received signal and perform eigenvalue decomposition to obtain the noise subspace of the received signal.

[0073] 21) The covariance matrix of the received signal is obtained using the maximum likelihood estimation method, and its expression is:

[0074]

[0075] Where R represents the covariance matrix of the received signal, K represents the number of snapshots, and H represents the matrix transpose.

[0076] 22) Perform eigenvalue decomposition on the covariance matrix.

[0077] Specifically, to separate the signal subspace from the noise subspace, the covariance matrix is ​​decomposed into eigenvalues, which can be expressed as:

[0078]

[0079] In the formula, U S and U N Representing the signal subspace and noise subspace respectively, Λ S and Λ N These are diagonal matrices composed of singular values. Without loss of generality, the signal subspace and the noise subspace are orthogonal.

[0080] Step 3: Construct a spectral peak search function in the angular dimension based on the noise subspace, and perform a dimensionality-reduced spectral peak search to obtain the angle estimate of the target.

[0081] 31) The dimensionality reduction transformation is constructed as follows:

[0082]

[0083]

[0084] In the formula, a T1 (θ,r) and a T2 (θ, r) represent the receiving direction vector a, respectively. T (θ,r) before L T One element and the remaining elements, a R1 (θ) and a R2(θ) represents the emission direction vector a R (θ) before L R One element and the remaining elements; L T and L R These represent the number of transmit antennas without amplitude loss and the number of receive antennas without phase loss, respectively. and Let represent the random amplitude and phase error vectors of the transmitting array and the receiving array, respectively, and 0 represent the zero matrix.

[0085] 32) Construct a spectral peak search function in the angular dimension, the expression of which is:

[0086]

[0087] In the formula,

[0088]

[0089] F1(θ) represents the spectral peak search function in the angular dimension, I M U represents a diagonal matrix of dimension M. N This represents the noise subspace.

[0090] It should be noted that the traditional MUSIC method directly obtains the estimates of angle and distance based on the orthogonality between the steering vector and the noise subspace, where the spectral peak search function can be expressed as:

[0091]

[0092] Then, the relationship between F1(θ) (abbreviated as F1) and F can be expressed as:

[0093]

[0094] 33) Based on the dimensionality reduction transformation and the spectral peak search function of the angular dimension, the spectral peak search after the dimensionality reduction transformation is performed to obtain the angle estimate of the target, the expression of which is:

[0095]

[0096] in, The value represents the estimated angle of the target, and det represents the determinant of the calculated matrix.

[0097] Step 4: Construct an angle-distance joint spectral peak search function based on the angle estimation, and perform spectral peak search to obtain the target distance estimate.

[0098] 41) Construct an angle-range joint spectral peak search function using the range dimension of the FDA-MIMO radar. Its expression is:

[0099]

[0100] In the formula,

[0101]

[0102] F2(θ,r) represents the angle-distance joint spectral peak search function.

[0103] The relationship between F2(θ,r) (abbreviated as F2) and F can be expressed as:

[0104]

[0105] in,

[0106]

[0107] 42) Based on the angle-distance joint spectral peak search function, a dimensionality-reduced spectral peak search is performed to obtain the target distance estimate, which is expressed as:

[0108]

[0109] in, This represents the estimated distance to the target.

[0110] Step 5: Obtain the eigenvector corresponding to the minimum eigenvalue of the angle-distance joint spectral peak search function.

[0111] In this embodiment, the sum matrix of the angle-distance joint spectral peak search function can be represented as:

[0112]

[0113] In the formula, F ct Let P represent the matrix corresponding to the sum of the angle-distance joint spectral peak search functions, where P represents the number of targets. -1 This represents finding the inverse of a matrix.

[0114] Specifically, step 5 includes:

[0115] Based on the relationship between the angle-distance joint peak search function F2(θ,r) and the peak search function F of the traditional MUSIC method, we have:

[0116]

[0117] Then matrix c TR The estimated value is a matrix. The eigenvector corresponding to the smallest eigenvalue.

[0118] Step 6: Construct a new matrix from the eigenvectors, and perform singular value decomposition on the new matrix to obtain the left and right singular matrices.

[0119] 61) Reconstruct the eigenvectors using the reshaping function to obtain the reconstruction matrix C. TR .

[0120] Because of c TR It is a vector that can be reshaped into a matrix C using a reshaping function. TR .

[0121] 62) Perform singular value decomposition on the reconstructed matrix, expressed as:

[0122] C TR =Q L Λ LR Q R ;

[0123] Among them, C TR Let Q represent the reconstructed matrix. L and Q R Let Λ represent the left and right singular matrices respectively. LR This represents a singular value matrix.

[0124] Step 7: Find the left and right singular value vectors corresponding to the largest singular value in the left and right singular matrices, and estimate the amplitude and phase errors of the transmit and receive arrays.

[0125] Specifically, by finding the left and right singular value vectors corresponding to the largest singular value in the left and right singular matrices, the error estimation formulas for the amplitude and phase of the transmit and receive arrays are expressed as follows:

[0126]

[0127]

[0128] in, The formulas for estimating the amplitude and phase of the transmitting array are given. The formula for estimating the amplitude and phase of the receiving array, q L and q R Let q represent the left and right singular value vectors corresponding to the maximum singular value, respectively. L (1) and q R (1) represent q respectively L and q R The first element.

[0129] This invention proposes a calibration and parameter estimation method for FDA-MIMO radar with random amplitude and phase errors. The method first calculates the covariance matrix of the received signal and performs eigenvalue decomposition to obtain the signal's noise subspace. Then, a dimensionality-reduced peak search method is used to estimate the target angle and range. Finally, singular value decomposition is performed on the sum matrix of the angle-range joint peak search function to obtain the left and right singular vectors corresponding to the maximum singular values, thereby obtaining the amplitude and phase error estimates. This method enables the localization and estimation of FDA-MIMO radar with random amplitude and phase errors, maintaining high-precision target estimation capabilities even for radar systems with amplitude and phase errors.

[0130] Example 2

[0131] Based on the above embodiment one, this embodiment provides a calibration and parameter estimation device for FDA-MIMO radar. Please refer to [link to embodiment one]. Figure 3 , Figure 3 This invention provides a structural block diagram of a calibration and parameter estimation device for an FDA-MIMO radar, comprising:

[0132] The matched filtering module is used to acquire the echo signal received by each receiving array element and perform matched filtering to obtain all received signals.

[0133] The first calculation module is used to calculate the covariance matrix of the received signal and perform eigenvalue decomposition to obtain the noise subspace of the received signal.

[0134] The angle estimation module is used to construct a spectral peak search function in the angle dimension based on the noise subspace, and perform spectral peak search after dimensionality reduction transformation to obtain the angle estimate of the target;

[0135] The distance estimation module is used to construct an angle-distance joint spectral peak search function based on the angle estimation, and to perform spectral peak search to obtain the target distance estimate;

[0136] The second calculation module is used to obtain the eigenvector corresponding to the minimum eigenvalue of the angle-distance joint spectral peak search function;

[0137] The singular value decomposition module is used to construct a new matrix from the eigenvectors and perform singular value decomposition on the constructed new matrix to obtain the left and right singular matrices.

[0138] The error estimation module is used to find the left and right singular value vectors corresponding to the largest singular value in the left and right singular matrices, and to perform error estimation of the amplitude and phase of the transmit and receive arrays.

[0139] The apparatus provided in this embodiment can implement the method provided in Embodiment 1 above. For details, please refer to Embodiment 1 above.

[0140] Therefore, this device has the ability to estimate targets with high accuracy even when amplitude and phase errors exist.

[0141] Example 3

[0142] This embodiment provides an FDA-MIMO radar system, including M transmitting elements and N receiving elements. The M transmitting elements are used to transmit orthogonal signals to the target, and the N receiving elements are used to receive echo signals returned from the target.

[0143] The radar system also includes: a processor, a communication interface, a memory, and a communication bus; among which,

[0144] The processor, communication interface, and memory communicate with each other through a communication bus;

[0145] Memory is used to store computer programs;

[0146] When the processor executes the program stored in the memory, it implements the method steps provided in Embodiment 1 above. For details, please refer to Embodiment 1 above.

[0147] Therefore, this radar system also has the ability to estimate targets with high accuracy.

[0148] Example 4

[0149] The effects of the present invention will be further explained below with reference to simulation experiments.

[0150] 1. Simulation parameters

[0151] The system simulation parameters used in this embodiment are shown in Table 1.

[0152] Table 1 Simulation parameters of the FDA-MIMO radar system

[0153]

[0154] 2. Simulation Content

[0155] The performance of the proposed method in FDA-MIMO radar is evaluated using several simulation results with amplitude and phase errors. The amplitude and phase errors are randomly chosen to satisfy a uniform distribution, while the real-valued ESPRIT method for FDA-MIMO radar is selected as a reference. The effect of uniform white Gaussian noise is also considered.

[0156] 3. Simulation Results and Analysis

[0157] Please see Figure 4-8 ,in, Figure 4This is a graph showing the estimation results for a three-target far-field scenario in a simulation experiment. The horizontal axis represents the angle, and the vertical axis represents the range. Figure 4 In this context, Actual Position represents the actual position, Theproposed represents the position estimated using the method of this invention, and ESPRIT and Unitary-ESPRIT represent the real-valued ESPRIT and the position corresponding to the ESPRIT method of the FDA-MIMO radar, respectively.

[0158] Figure 5 and Figure 6 The figures show the amplitude and phase error estimation results for the transmitting array elements. Figure 7 and Figure 8 The figures show the estimation results of amplitude and phase errors for the receiving array elements. The horizontal axis represents the element index, and the vertical axis represents the amplitude error and phase error. In the figures, True Value represents the true value, and Estimated Value represents the estimated value. It can be seen that the estimation results using the method of this invention are very close to the true values, while the estimation results of ESPRIT and real-valued ESPRIT are randomly distributed.

[0159] It should be noted that the comparison method does not have the ability to estimate amplitude and phase errors, and therefore these were not plotted. By comparing the results with those of the comparison method, the results show that the method of this invention has better positioning performance.

[0160] Furthermore, Figure 9 and Figure 10 The root mean square errors (RMSE) for range and angle are given. The horizontal axis represents the signal-to-noise ratio (SNR), and the vertical axis represents the RMSE of Range and RMSE of Angle, respectively. For comparison, the FDA-MIMO radar's Cramer-Rao boundary is also plotted. The number of snapshots in this section is set to 200. Figure 9 and Figure 10 It can be seen that the angle estimation accuracy using the method of this invention is closer to CRLB than ESPRIT and real-valued ESPRIT.

[0161] Figure 11 and Figure 12The root mean square (RMSE) values ​​for target localization distance and angle were analyzed. The x-axis represents the number of snapshots, and the y-axis represents the RMSE of Range and RMSE of Angle, respectively. With the target's signal-to-noise ratio (SNR) fixed at 10 dB, the changes in the RMSE curves as the number of snapshots increased from 100 to 1100 were shown. This method was compared with ESPRIT and real-valued ESPRIT. The results show that this method approaches CRLB (Common Root Mean Square) as the number of snapshots increases, and the comparison method fails under these conditions.

[0162] The simulation results above show that existing methods fail completely in the presence of random amplitude and phase errors, while the estimation method of this invention still maintains high-efficiency target localization performance.

[0163] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A calibration and parameter estimation method for an FDA-MIMO radar, characterized in that, include: Step 1: Obtain the echo signal received by each receiving array element and perform matched filtering to obtain all received signals; Step 2: Calculate the covariance matrix of the received signal and perform eigenvalue decomposition to obtain the noise subspace of the received signal; Step 3: Construct an angular-dimensional spectral peak search function based on the noise subspace, and perform a dimensionality-reduced spectral peak search to obtain the target's angle estimate; wherein, the dimensionality-reduced transformation is expressed as: ； ； In the formula, and Let represent the diagonal matrices containing the amplitude and phase errors in the receiving array and transmitting array, respectively. and These represent the receiving direction vectors respectively. The former One element and the remaining elements, and These represent the launch direction vectors respectively. The former The elements and the remaining elements, and These represent the number of transmit antennas without amplitude loss and the number of receive antennas without phase loss, respectively. and Let these represent the random amplitude and phase error vectors of the transmitting array and the receiving array, respectively. Represents a zero matrix; Indicates the number of transmitting array elements. Indicates the number of receiving array elements. From the perspective of the target, Indicates the distance to the target. Represents a diagonal matrix; Step 4: Based on the angle estimation, construct the angle-range joint spectral peak search function using the range dimension degree of freedom of the FDA-MIMO radar, and perform spectral peak search to obtain the target range estimate; Step 5: Based on the relationship between the angle-distance joint peak search function and the peak search function of the traditional MUSIC method, obtain the feature vector corresponding to the minimum feature value of the angle-distance joint peak search function; wherein, the angle-distance joint peak search function... Compared with the traditional MUSIC method peak search function The relationship is represented as: ； In the formula, ； Then reconstruct the matrix The estimated value is a matrix. The eigenvector corresponding to the smallest eigenvalue. This represents the Kronecker product operation; Step 6: Use the reshaping function to construct a new matrix from the eigenvectors, and perform singular value decomposition on the constructed new matrix to obtain the left and right singular matrices; Step 7: Find the left and right singular value vectors corresponding to the largest singular value in the left and right singular matrices, and normalize the left and right singular value vectors according to the first element of the left and right singular value vectors respectively to obtain the error estimates of the amplitude and phase of the transmit and receive arrays.

2. The calibration and parameter estimation method for an FDA-MIMO radar according to claim 1, characterized in that, In step 1, the first m The transmitted signal passes through the first n The received signal after filtering by each receiving element is represented as follows: Its expression is: ； In the formula, , Indicates the number of transmitting array elements. , Indicates the number of receiving array elements. Indicates the radar's transmission power. The complex coefficients representing the target. Represents the speed of light. From the perspective of the target, Indicates the distance to the target. This indicates the frequency offset between adjacent antennas. Indicates the carrier frequency. and These represent the spacing between the elements of the transmitting array and the receiving array, respectively. The vector form of the filtered received signal Represented as: ； in, This represents the transpose operator. The Kronecker product represents the transmit and receive steering vectors with amplitude and phase errors. Represents white noise. and These are the transmit and receive direction vectors, respectively. and The diagonal matrix representing the amplitude and phase errors contained in the receiving and transmitting arrays. This represents the Kronecker product operation.

3. The calibration and parameter estimation method for an FDA-MIMO radar according to claim 2, characterized in that, Step 2 includes: 21) The covariance matrix of the received signal is obtained using the maximum likelihood estimation method, and its expression is: ； in, This represents the covariance matrix of the received signal. K Indicates the number of snapshots. H Indicates matrix transpose; 22) Perform eigenvalue decomposition on the covariance matrix, expressed as: ； In the formula, and Representing the signal subspace and noise subspace respectively, and These are diagonal matrices composed of singular values.

4. The calibration and parameter estimation method for an FDA-MIMO radar according to claim 3, characterized in that, Step 3 includes: 31) Construct a spectral peak search function in the angular dimension, the expression of which is: ； In the formula, ； Describes the spectral peak search function in the angular dimension. The dimension is diagonal matrix, Represents the noise subspace; 32) Based on the dimensionality reduction transformation and the spectral peak search function of the angular dimension, perform spectral peak search after the dimensionality reduction transformation to obtain the angle estimate of the target, the expression of which is: ； in, The value represents the estimated angle of the target, and det represents the determinant of the calculated matrix.

5. The calibration and parameter estimation method for an FDA-MIMO radar according to claim 4, characterized in that, Step 4 includes: 41) Construct an angle-range joint spectral peak search function using the range dimension of the FDA-MIMO radar. Its expression is: ； In the formula, ； This represents the angle-distance joint spectral peak search function; 42) Based on the angle-distance joint spectral peak search function, a dimensionality-reduced spectral peak search is performed to obtain the target distance estimate, which is expressed as: ； in, This represents the estimated distance to the target.

6. The calibration and parameter estimation method for an FDA-MIMO radar according to claim 1, characterized in that, Step 6 includes: 61) Reconstruct the eigenvectors using the reshaping function to obtain the reconstruction matrix. ; 62) Perform singular value decomposition on the reconstructed matrix, expressed as: ； in, Represents the reconstructed matrix. and Let them represent the left and right singular matrices, respectively. This represents a singular value matrix.

7. The calibration and parameter estimation method for an FDA-MIMO radar according to claim 6, characterized in that, Step 7 includes: In the left and right singular matrices, by finding the left and right singular value vectors corresponding to the largest singular value, the error estimation formulas for the amplitude and phase of the transmit and receive arrays are expressed as follows: ； ； in, The formulas for estimating the amplitude and phase of the transmitting array are given. The formulas for estimating the amplitude and phase of the receiving array are given. and These represent the left and right singular value vectors corresponding to the maximum singular value, respectively. and They represent and The first element.

8. A calibration and parameter estimation apparatus for an FDA-MIMO radar, used to implement the method of claim 1, characterized in that, The device includes: The matched filtering module is used to acquire the echo signal received by each receiving array element and perform matched filtering to obtain all received signals. The first calculation module is used to calculate the covariance matrix of the received signal and perform eigenvalue decomposition to obtain the noise subspace of the received signal. An angle estimation module is used to construct a spectral peak search function in the angle dimension based on the noise subspace, and perform a spectral peak search after dimensionality reduction transformation to obtain the angle estimate of the target; The range estimation module is used to construct an angle-range joint spectral peak search function based on the angle estimation and the range dimension degree of freedom of the FDA-MIMO radar, and to perform spectral peak search to obtain the target range estimate. The second calculation module is used to obtain the feature vector corresponding to the minimum feature value of the angle-distance joint spectral peak search function based on the relationship between the angle-distance joint spectral peak search function and the spectral peak search function of the traditional MUSIC method. The singular value decomposition module is used to construct a new matrix from the eigenvectors using a reshaping function, and to perform singular value decomposition on the constructed new matrix to obtain left and right singular matrices. The error estimation module is used to find the left and right singular value vectors corresponding to the largest singular value in the left and right singular matrices, and to normalize the left and right singular value vectors according to the first element of the left and right singular value vectors respectively, so as to obtain the error estimates of the amplitude and phase of the transmit and receive arrays.

9. An FDA-MIMO radar system, characterized in that, include M Each launch element and N Each receiving array element, the M Each transmitting element is used to transmit orthogonal signals to the target. N Each receiving array element is used to receive the echo signal returned from the target; The radar system further includes: a processor, a communication interface, a memory, and a communication bus; wherein, The processor, communication interface, and memory communicate with each other through a communication bus; Memory is used to store computer programs; When the processor executes a program stored in memory, it implements the method described in any one of claims 1-7.

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